This isn't what you are trying to do. You want to find the kernel of the map L, which will be a 4-by-4 matrix but you don't want to think of it that way. You need to solve,\(\displaystyle

L\left(\begin{bmatrix}a&b\\c& d\end{bmatrix}\right)\) \(\displaystyle

\left(\begin{bmatrix}x\\y\\z\end{bmatrix}\right)

\) = 0?

I'm lost because I know it's not possible to multiply a 2x2 matrix by a 3x2 matrix

\(\displaystyle L(M)=0 \Rightarrow \ldots\).

This is basically asking you if \(\displaystyle ax^3+bx^2+cx+d = 0\) then what are \(\displaystyle a, b, c\) and \(\displaystyle d\)?

Last edited: